Momentum and Impulse

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Momentum

Momentum: Mass (kg) x Velocity (m/s) , units are $kg$ $m{s}^{-1}$

• Vector quantity, include direction

$p=mv$

Rate of Change

• The rate of change of momentum of an object is equal to the force applied to the object

$\frac{\Delta p}{t}=\frac{p_f-p_i}{t}$

$=\frac{m(v-u)}{t}$

$=(\frac{v-u}{t})m$

$=ma=F$

Momentum is conserved

• Law of Conservation of Mass: mass is not created nor destroyed, only combined with mass/energy
• Law of Conservation of Energy: energy cannot be created nor destroyed, only transformed or transferred

Momentum cannot be created nor destroyed

∴ Total momentum before an event = Total momentum after an event

$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

Impulse

• Change in momentum
  • Include direction
• Product of force and time
• $N\times s$, or $Newtons\times seconds$
• Can also be written as $kg$ $m{s}^{-1}$

$j=Ft$

$j=\Delta p=m(v-u)$